Theorems · Theorem · group theory
AddSubmonoid.coe_finsetSum
∀ {ι : Type u_4} {M : Type u_5} [inst : AddCommMonoid M] (S : AddSubmonoid M) (f : ι → ↥S) (s : Finset ι),
↑(∑ i ∈ s, f i) = ∑ i ∈ s, ↑(f i)- Cited by
- 5 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Quot.sound
- Assumes
- AddCommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- AddCommMonoidstatement and proof · cited by 12,281
- Finset.sumstatement · cited by 5,195
- AddSubmonoidstatement and proof · cited by 1,178
- map_sumproof · cited by 455
- AddSubmonoid.subtypeproof · cited by 28
Cited by5
Results whose statement or proof uses this declaration.
- Submodule.mem_set_smulproof · cited by 1
- Submodule.set_smul_eq_mapproof · cited by 1
- AddSubmonoid.coe_finset_sumproof · cited by 0
- SimpleGraph.linearIndependent_lapMatrix_ker_basis_auxproof · cited by 0
- SimpleGraph.top_le_span_range_lapMatrix_ker_basis_auxproof · cited by 0